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Simplifying x2 + x + (x + -10) + (x + 1) + ([x + -10] + -14) = 30 Reorder the terms: x2 + x + (-10 + x) + (x + 1) + ([x + -10] + -14) = 30 Remove parenthesis around (-10 + x) x2 + x + -10 + x + (x + 1) + ([x + -10] + -14) = 30 Reorder the terms: x2 + x + -10 + x + (1 + x) + ([x + -10] + -14) = 30 Remove parenthesis around (1 + x) x2 + x + -10 + x + 1 + x + ([x + -10] + -14) = 30 Reorder the terms: x2 + x + -10 + x + 1 + x + ([-10 + x] + -14) = 30 Remove brackets around [-10 + x] x2 + x + -10 + x + 1 + x + (-10 + x + -14) = 30 Reorder the terms: x2 + x + -10 + x + 1 + x + (-10 + -14 + x) = 30 Combine like terms: -10 + -14 = -24 x2 + x + -10 + x + 1 + x + (-24 + x) = 30 Remove parenthesis around (-24 + x) x2 + x + -10 + x + 1 + x + -24 + x = 30 Reorder the terms: -10 + 1 + -24 + x + x + x + x + x2 = 30 Combine like terms: -10 + 1 = -9 -9 + -24 + x + x + x + x + x2 = 30 Combine like terms: -9 + -24 = -33 -33 + x + x + x + x + x2 = 30 Combine like terms: x + x = 2x -33 + 2x + x + x + x2 = 30 Combine like terms: 2x + x = 3x -33 + 3x + x + x2 = 30 Combine like terms: 3x + x = 4x -33 + 4x + x2 = 30 Solving -33 + 4x + x2 = 30 Solving for variable 'x'. Reorder the terms: -33 + -30 + 4x + x2 = 30 + -30 Combine like terms: -33 + -30 = -63 -63 + 4x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -63 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 4x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 4x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 4x + x2 = 0 + 63 4x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 4x + x2 = 63 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 63 + 4 Reorder the terms: 4 + 4x + x2 = 63 + 4 Combine like terms: 63 + 4 = 67 4 + 4x + x2 = 67 Factor a perfect square on the left side: (x + 2)(x + 2) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 2) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 2 = 8.185352772 Simplifying x + 2 = 8.185352772 Reorder the terms: 2 + x = 8.185352772 Solving 2 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.185352772 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.185352772 + -2 x = 8.185352772 + -2 Combine like terms: 8.185352772 + -2 = 6.185352772 x = 6.185352772 Simplifying x = 6.185352772Subproblem 2
x + 2 = -8.185352772 Simplifying x + 2 = -8.185352772 Reorder the terms: 2 + x = -8.185352772 Solving 2 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.185352772 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.185352772 + -2 x = -8.185352772 + -2 Combine like terms: -8.185352772 + -2 = -10.185352772 x = -10.185352772 Simplifying x = -10.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.185352772, -10.185352772}
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